Math Problem Statement
An oxygen tank is constructed of a right cylinder of height y and radius x with two hemispheres of radius x mounted on the top and bottom of the cylinder. Express the volume in units3 of the cylinder as a function of two variables, x and y.
V(x, y) = units3
Find
V(15, 3). units3
Explain what this means.
This means that a tank with cylinder height and radius has volume units3.
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of Cylinders
Volume of Spheres
Formulas
Volume of a cylinder: V_cylinder = πx^2y
Volume of a sphere: V_sphere = (4/3)πx^3
Total volume of the tank: V(x, y) = πx^2y + (4/3)πx^3
Theorems
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Suitable Grade Level
Grades 10-12
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